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Revision History for A359541

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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Inverse Möbius transform of A328308, which is the characteristic function of numbers that eventually reach zero when iterated with the arithmetic derivative.
(history; published version)

#10 by Michael De Vlieger at Thu Jan 05 18:27:22 EST 2023

STATUS

proposed

approved

#9 by Antti Karttunen at Thu Jan 05 15:41:12 EST 2023

STATUS

editing

proposed

#8 by Antti Karttunen at Thu Jan 05 11:13:59 EST 2023

LINKS

Antti Karttunen, <a href="/A359541/b359541.txt">Table of n, a(n) for n = 1..65537</a>

STATUS

approved

editing

#7 by Michael De Vlieger at Thu Jan 05 10:54:05 EST 2023

STATUS

proposed

approved

#6 by Antti Karttunen at Thu Jan 05 10:51:38 EST 2023

STATUS

editing

proposed

#5 by Antti Karttunen at Thu Jan 05 07:38:50 EST 2023

FORMULA

a(n) = A000005(n) - A359542(n).

CROSSREFS

Cf. A000005, A328308, A328309, A359542.

#4 by Antti Karttunen at Thu Jan 05 07:30:49 EST 2023

FORMULA

a(n) < A328309(n).

CROSSREFS

Cf. A328308, A328309.

#3 by Antti Karttunen at Thu Jan 05 07:28:52 EST 2023

NAME

allocated for Antti KarttunenInverse Möbius transform of A328308, which is the characteristic function of numbers that eventually reach zero when iterated with the arithmetic derivative.

DATA

1, 2, 2, 2, 2, 4, 2, 2, 3, 4, 2, 4, 2, 4, 3, 2, 2, 6, 2, 4, 4, 4, 2, 4, 3, 3, 3, 4, 2, 7, 2, 2, 4, 4, 3, 6, 2, 4, 3, 4, 2, 8, 2, 4, 4, 4, 2, 4, 3, 5, 3, 3, 2, 6, 3, 4, 4, 4, 2, 7, 2, 4, 5, 2, 4, 8, 2, 4, 3, 7, 2, 6, 2, 3, 4, 4, 4, 6, 2, 4, 3, 4, 2, 8, 4, 3, 3, 4, 2, 9, 3, 4, 4, 4, 3, 4, 2, 6, 5, 5, 2, 6, 2, 3, 6

OFFSET

1,2

FORMULA

a(n) = Sum_{d|n} A328308(d).

PROG

(PARI)

A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));

A328308(n) = if(!n, 1, while(n>1, n = A003415checked(n)); (n));

A359541(n) = sumdiv(n, d, A328308(d));

CROSSREFS

Cf. A328308.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jan 05 2023

STATUS

approved

editing

#2 by Antti Karttunen at Thu Jan 05 07:24:02 EST 2023

KEYWORD

allocating

allocated

#1 by Antti Karttunen at Thu Jan 05 07:24:02 EST 2023

NAME

allocated for Antti Karttunen

KEYWORD

allocating

STATUS

approved